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Estimation of CN Parameter for Small Agricultural Watersheds Using Asymptotic Functions

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Estimation of CN Parameter for Small Agricultural Watersheds Using Asymptotic Functions Water 2015, 7, 939-955; doi:10.3390/w7030939 OPEN ACCESS water ISSN 2073-4441 www.mdpi.com/journal/water Article Estimation of CN Parameter for Small Agricultural Watersheds Using Asymptotic Functions Tomasz Kowalik 1 and Andrzej Walega 2,* 1 Department of Land Reclamation and Environmental Development, University of Agriculture in Krakow, St. Mickiewicza 24-28, Krakow 30-050, Poland; E-Mail: [email protected] 2 Department of Sanitary Engineering and Water Management, University of Agriculture in Krakow, St. Mickiewicza 24-28, Krakow 30-058, Poland * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +48-012-662-4102. Academic Editor: Richard Smardon Received: 26 January 2015 / Accepted: 2 March 2015 / Published: 10 March 2015 Abstract: This paper investigates a possibility of using asymptotic functions to determine the value of curve number (CN) parameter as a function of rainfall in small agricultural watersheds. It also compares the actually calculated CN with its values provided in the Soil Conservation Service (SCS) National Engineering Handbook Section 4: Hydrology (NEH-4) and Technical Release 20 (TR-20). The analysis showed that empirical CN values presented in the National Engineering Handbook tables differed from the actually observed values. Calculations revealed a strong correlation between the observed CN and precipitation (P). In three of the analyzed watersheds, a typical pattern of the observed CN stabilization during abundant precipitation was perceived. It was found that Model 2, based on a kinetics equation, most effectively described the P-CN relationship. In most cases, the observed CN in the investigated watersheds was similar to the empirical CN, corresponding to average moisture conditions set out by NEH-4. Model 2 also provided the greatest stability of CN at 90% sampled event rainfall. Keywords: agricultural watershed; rainfall-runoff model; CN parameter; asymptotic equation; SCS method Water 2015, 7 940 1. Introduction The runoff amount from an ungauged watershed is one of the basic hydrological parameters used in hydraulic engineering design, flood protection, or in the process of modeling of watershed water balance components [1–8]. Originally, storm water runoff from small agricultural watersheds was estimated using the Soil Conservation Service (SCS) curve number (CN) method, developed by the United State Department of Agriculture (USDA). This method is currently known as the Natural Resources Conservation Service (NRCS)-CN method. Furthermore, its scope has expanded beyond the evaluation of storm runoff and it has become an integral part of more complex, long-term simulation models [9]. This method represents an event-based lumped conceptual approach [10–16]. In the words of Ponce and Hawkins [17] “The SCS-CN method is a conceptual model of hydrologic abstraction of storm rainfall, supported by empirical data. Its objective is to estimate direct runoff volume from storm rainfall depth, based on a curve number CN”. Despite widespread use of SCS-CN methodology, realistic estimation of the CN parameter has been widely discussed among hydrologists and water resources community [18–24]. The SCS-CN is a very simple approach developed for predicting surface runoff from hortonian overland flow dominated watersheds. It is straightforward and easy to apply. A primary reason for its wide applicability and acceptability is the fact that it accounts for major runoff generating watershed characteristics, namely soil type, land use/treatment, surface conditions and antecedent moisture conditions (AMC)[4,25–29]. Currently, this method is included in widely used hydrological software, such as WinTR55, WinTR20, HEC-HMS, EPA-SWMM, SWAT, GLEAMS, EPIC, NLEAP, and AGNPS [30], and it is consequently applied in a large number of scientific studies. Isik et al. [31] used a hybrid model based on Artificial Neural Networks (ANNs), and SCS-CN to predict the effect of changes in land use/cover on daily streamflow. Kabiri et al. [32] claimed that runoff values determined by means of the SCS-CN method did not differ from those calculated with the Green-Ampt method. Grimaldi et al. [33,34] proposed a method combining the Green-Ampt infiltration equation and calibration of both the ponding time and soil hydraulic conductivity, using the initial abstraction and total volume given by the SCS-CN method. Sahu et al. [35] verified modified versions of the SCS method to estimate the runoff in agricultural watersheds. The modification involved a different way of determining soil moisture conditions in relation to the original method. Soulis et al. [36] reported a strong correlation between the CN parameter and the precipitation (P) amount, i.e., the more abundant the precipitation, the lower the CN. They also found that flow amount, determined by means of the original method, was markedly overestimated in relation to empirical values and underestimated for scant precipitations. Banasik et al. [37] claimed that application of the SCS-CN method should rely on deep insight into the probabilistic properties of CN and maximum potential retention S. However, estimating watershed runoff based on the original SCS method is disputable. The greatest limitations of the original SCS-CN method include possible sudden jumps in the computed runoff due to using three AMC levels permitting unreasonable sudden jumps in CN, lack of clear guidance on how to vary antecedent moisture conditions, and no explicit dependency between the initial abstraction and the antecedent moisture [35]. Woodward et al. [38] indicated that the SCS-CN method was not applicable at sub-daily time resolution. Hawkins [39] reported that the runoff calculated from the SCS method was much more sensitive to the CN chosen than to rainfall depths. Therefore, error analysis and sensitivity Water 2015, 7 941 calculus seem to indicate that errors in CN affect the runoff calculation to a much greater extent than errors in the storm rainfall. Next, it is difficult to correctly select CNs from available handbook tables. CNs from the handbook tables is most successfully estimated for traditional agricultural watersheds, less successfully for semiarid rangelands and the least successfully for forest watersheds. Numerous studies on the application of the original SCS-CN method for calculating effective rainfall [40–42] showed that CN parameter values, specified theoretically and according to SCS guidelines, differed significantly from those calculated empirically, based on recorded rainfall-runoff events. Apart from variable watershed moisture conditions, the CN parameter is also affected by precipitation abundance, which is not accounted for in the original method. In his study on asymptotic determination of runoff curve numbers from measured runoff, Hawkins [39] concluded that a secondary systematic correlation usually emerged in watersheds between the calculated CN value and the rainfall depth. In most watersheds, the calculated CNs approaches a constant value with increasing rainfall depth that is assumed to characterize a specific watershed. The three different patterns of the CN-P relationship can be described as follows: the most common scenario is that small rainfall depths correspond to greater values of calculated CNs, which decline progressively with increasing storm size, approaching a stable near constant asymptotic CN value with increasingly larger storms. This behavior occurs most frequently and it is deemed “standard”. In less common cases, the observed CN declines steadily with increasing rainfall, with no appreciable tendency to approach a constant value (“complacent” behavior). In the last case, also concerning a small number of watersheds, the calculated CNs has an apparently constant value for all rainfall depths, except for very low rainfall depths where CN increases suddenly (“violent” behavior). Soulis et al. [43,44], used a two-CN heterogeneous system for calculating watershed runoff. They found that in the watersheds characterized by heterogeneous land use, the runoff determined with this approach was very similar to the actually recorded runoff. They also demonstrated that the runoff calculated with the proposed method allowed—irrespective of the adopted λ value—a more accurate runoff evaluation as compared with the original SCS-CN method. Unfortunately, many designers unknowingly use the original method in their hydrological calculations, which can result in a significant underestimation of the actual flood parameters. Therefore, it seems necessary to verify the application of the SCS-CN approach in local conditions, to reduce the uncertainty of modeling results and to promote more common use of this method in practice. The aim of the study was to assess the applicability of asymptotic functions for determining the value of the CN parameter as a function of precipitation depth in small agricultural watersheds. Additionally, a comparative analysis of the computed CN values and those provided by SCS National Engineering Handbook Section 4(NEH-4) Hydrology and Technical Release 20 (TR-20) was carried out. The methodological basis of this work was the research published by Hawkins [39]. The methods described there were supplemented with so far uncommonly used asymptotic functions such as kineticsfunction and complementary error function peak from the set of symmetric functions. 2. Materials and Methods The study was conducted in four small watersheds, two of which (A and D) are located in Gaj, the municipality of Mogilany,
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